Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
12.3k views
in Physics by (58.2k points)

An open belt running over two pulleys 24cm and 60cm diameters. Connects two parallel shaft 3m apart and transmits 3.75KW from the smaller pulley that rotates at 300RPM, µ = 0.3, and the safe working tension in 100N/cm width. Determine 

(i) Minimum width of the belt. 

(ii) Initial belt tension. 

(iii) Length of the belt required.

1 Answer

+1 vote
by (66.1k points)
selected by
 
Best answer

Given that, 

D1 = 60cm 

D2 = 24cm 

N2 = 300rpm µ = 0.3 

X = 3m = 300cm 

P = 3.75KW

Safe Tension = Maximum tension = 100N/cm width = 100b N b = width of belt 

Tmax = 100b  ...(i)

Let θ = Angle of contact

Sinα = (r1 – r2)/X = (30 – 12)/300 ; α = 3.45°, ...(ii)

 = Π – 2α = (180 – 2 X 3.45) = 173.1°

= (173.1°)X Π/180 = 3.02 rad ......(iii)

Now,

Using the relation, Ratio of belt tension = T1/T2 = eµθ = e(0.3)(3.02)

T1 = 2.474 T2 ......(iv)

Now,

V = πDN/60 m/sec, D is in meter and N is in RPM

 = 3.14 X (0.24)(300)/60 = 3.77m/sec ......(v)

Power Transmitted (P) = (T1 – T2).v/1000 Kw

3.75 = (T1 – T2)X 3.77/1000

T1 – T2 = 994.7N .......(vi)

 From relation (iv) and (v), we get:

T1 = 1669.5N ...........(vii)

T2 = 674.8N ...........(viii)

(i) For width of the belt 

But T1 = Tmax = 100b; 1669.5 = 100b; b = 16.7cm 

(ii) For initial tension in the belt 

Let To = initial tension in the belt

To = (T1 + T2)/2

= (1669.5 + 674.8)/2

To = 1172.15N

(iii) For length of belt

Putting all the value, we get

L = 7.33m.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...